1. The Field of the Invention
The present disclosure relates in general to the imaging of different physical properties of geological formations, human and/or animal bodies, and/or man-made objects. The present disclosure can be applied to geophysical imaging, medical imaging, nondestructive imaging, and remote sensing.
2. The Related Technology
Methods of geophysical, medical, and nondestructive imaging are based on parameterizing models in terms of physical properties that can predict the observed data so as to minimize a parametric functional with both misfit and stabilizing functional terms. Given the ill-posedness of the inverse problems encountered in geophysical, medical, and nondestructive imaging, a variety of regularization methods are introduced to obtain unique and stable inverse solutions. The state-of-the-art in inverse problem solution and regularization theory is detailed by Zhdanov, 2002, 2009.
Conventional inverse methods characterize the model parameters of an examined medium by a function of the physical properties which varies continuously within known bounds, which in some applications, may be inadequate for imaging objects with discrete physical properties.
In many practical applications, the goal of inversion is to find at least one target with sharp boundaries and strong physical property contrasts between the targets and the host medium. For example, there exists a significant physical property contrast between an air-filled tunnel and surrounding earth, or between a defect within a concrete or metal fabrication and the surrounding medium, or between a diseased human heart or bone or malignant tumor and other human tissue and bone.
Conventional inversion methods cannot be used to image objects with discrete physical properties, because parameterization with discrete physical properties prevents differentiation of the observed data with respect to the physical properties, thus preventing the use of efficient gradient-based optimization methods. Rather, stochastic optimization methods could be used, but stochastic optimization methods involve computationally intensive modeling, which makes them inefficient or even impractical to implement, particularly for real-time imaging applications.
For geophysical, medical, and nondestructive imaging, particularly for real-time applications and/or where the inverse problem is highly constrained by known physical property values, there exists a need to develop an imaging method that parameterizes the models in terms of discrete physical properties yet enables the use of efficient gradient-type optimization methods, thus preserving all of the established advantages of regularized imaging methods.